You inherit one copy of each pair of chromosomes 1 to 22 from your mother and one from your father. These account for about 95% of your DNA. If you have relatively recent mixed ancestry you will be carrying blocks of DNA from different continents.
For example if your mother was British and your father Nigerian, then one copy of each chromosome will be African in origin and one copy European.
If the mixed ancestry is further back in time, e.g. if one grandfather was European, with three grandparents SE Asian, then about half of the blocks on one copy of each chromosome will be East Asian, the rest being European.
As we go further back, the total length of DNA from the mixture decreases until eventually after 8 or more generations it can be gone entirely. Although your parents inherit half their DNA from your grandparents, because it is random which of their copies you inherit at any given place along the chromosomes, you can by chance get more DNA from one grandparent than from another. Over the generations this effect means that eventually you have pedigree ancestors who contributed no DNA to you, conversely other pedigree ancestors contributed more than would be predicted by chance. Hence the proportion of DNA from different ancestries can be very variable, and differs among siblings for example.
The graphic shows the two copies of each chromosome, from the largest chromosome (1) at the top to the smaller ones at the bottom. These are coloured according to the inferred ancestry of the segments of chromosome – shown in the map.
How does it work? We first use a statistical model to separate the DNA markers you inherited from your mother and father. These then undergo a principal components-based analysis in a sliding window across the chromosomes, followed by a smoothing procedure.